I agree that you're really vulnerable. You don't even have to imagine that he has bad intentions to think this is true: if (God forbid) he got hit by a bus tomorrow, you would be in a tight spot about taxation, pension, and employment.
(I can be cynical about this: I think it also makes the power differential enormous, with him having the ability to hold your livelihood over your decisions; it's a lot harder to leave someone when you'd be financially rinsed by that choice. But let's set cynicism to the side.)
He needs to do the right thing by your family.* That thing is to marry you so that you can get all the contractual cover of a marriage. It does not have to be a big deal, nor does it have to be a wedding, but it has to happen.
If not, you need to make arrangements, now, to go back to work. You need to retrain and to get a job with a sufficient income to support you and your kids. And he will need to pay half for childcare and do half the other household chores. If your child having SN means this isn't possible, then he can help pay for full-time childcare, then he can go part-time with you so that one of you is always home. It's a choice he can make, if he feels the need to do so.
It won't make you feel cherished, and it won't make you emotionally satisfied. I'm so sorry about this. I get that it's not just that you want to be married to him, it's that you want him to want to be married. You can't control that. But it will make you financially secure, which is the hard-nosed important thing to do.
*Please note that I say the right thing by your family. For some families, marriage doesn't make sense; for others, its practicalities are neutral and it's up to the people to decide. But in your situationSAHM, built all assets together, SN child, about to buy a house, no financial separation or independenceit's vital.